Advanced Financial Mathematics question need help pls

Let : [0,00) [0, 1] be a generator of a d-dimensional Archimedean copula C. a) Show that limo (t) = 0 must hold. b) Show that (0) = 1 must hold. c) Show that (ct), t 0, generates C for all c> 0. d) Show that the lower tail dependence coefficient of the bivariate copula satisfies X = lim,(t) (21) Let : [0,00) [0, 1] be a generator of a d-dimensional Archimedean copula C. a) Show that limo (t) = 0 must hold. b) Show that (0) = 1 must hold. c) Show that (ct), t 0, generates C for all c> 0. d) Show that the lower tail dependence coefficient of the bivariate copula satisfies X = lim,(t) (21)